Year: 2025
Type: preprint
Abstract: This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs auxiliary space preconditioning and regular decompositions to decompose the finite element residual into $H^{-1}$ residuals that are further controlled by classical p-robust equilibrated a posteriori error analysis. As a result, we obtain novel and simple p-robust a posteriori error estimates of $H(\rm curl)$/$H(\rm div)$ conforming methods and mixed methods for the biharmonic equation. In addition, we prove guaranteed a posteriori upper error bounds under convex domains or certain boundary conditions. Numerical experiments demonstrate the effectiveness and p-robustness of the proposed error estimators for the Nédélec edge element methods and the Hellan--Herrmann--Johnson methods.
Source: arXiv (Cornell University)
Author: Li, Yuwen
Institution: Zhejiang University
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Award: G5611576681
OpenAlex ID: W7104889096
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